Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

On-site data cast doubts on the hypothesis of shifting cultivation in the Late Neolithic (c. 4300-2400 cal. BC): Landscape management as an alternative paradigm

This article brings together in a comprehensive way, and for the first time, on- and off-site palaeoenvironmental data from the area of the Central European lake dwellings (a UNESCO World Cultural Heritage Site since 2011). The types of data considered are as follows: high-resolution off-site pollen cores, including micro-charcoal counts, and on-site data, including botanical macro- and micro-remains, hand-collected animal bones, remains of microfauna, and data on woodland management (dendrotypology). The period considered is the late Neolithic (c. 4300–2400 cal. BC). For this period, especially for its earlier phases, discussions of land-use patterns are contradictory. Based on off-site data, slash-and-burn – as known from tropical regions – is thought to be the only possible way to cultivate the land. On-site data however show a completely different picture: all indications point to the permanent cultivation of cereals (Triticum spp., Hordeum vulgare), pea (Pisum sativum), flax (Linum usitatissimum) and opium-poppy (Papaver somniferum). Cycles of landscape use are traceable, including coppicing and moving around the landscape with animal herds. Archaeobiological studies further indicate also that hunting and gathering were an important component and that the landscape was manipulated accordingly. Late Neolithic land-use systems also included the use of fire as a tool for opening up the landscape. Here we argue that bringing together all the types of palaeoenvironmental proxies in an integrative way allows us to draw a more comprehensive and reliable picture of the land-use systems in the late Neolithic than had been reconstructed previously largely on the basis of off-site data

Chemical analysis of pottery demonstrates prehistoric origin for high-altitude alpine dairying

The European high Alps are internationally renowned for their dairy produce, which are of huge cultural and economic significance to the region. Although the recent history of alpine dairying has been well studied, virtually nothing is known regarding the origins of this practice. This is due to poor preservation of high altitude archaeological sites and the ephemeral nature of transhumance economic practices. Archaeologists have suggested that stone structures that appear around 3,000 years ago are associated with more intense seasonal occupation of the high Alps and perhaps the establishment of new economic strategies. Here, we report on organic residue analysis of small fragments of pottery sherds that are occasionally preserved both at these sites and earlier prehistoric rock-shelters. Based mainly on isotopic criteria, dairy lipids could only be identified on ceramics from the stone structures, which date to the Iron Age (ca. 3,000 - 2,500 BP), providing the earliest evidence of this practice in the high Alps. Dairy production in such a marginal environment implies a high degree of risk even by today’s standards. We postulate that this practice was driven by population increase and climate deterioration that put pressure on lowland agropastoral systems and the establishment of more extensive trade networks, leading to greater demand for highly nutritious and transportable dairy products

SARS-CoV-2 outbreak in a tri-national urban area is dominated by a B.1 lineage variant linked to a mass gathering event.

The first case of SARS-CoV-2 in Basel, Switzerland was detected on February 26th 2020. We present a phylogenetic study to explore viral introduction and evolution during the exponential early phase of the local COVID-19 outbreak from February 26th until March 23rd. We sequenced SARS-CoV-2 naso-oropharyngeal swabs from 746 positive tests that were performed at the University Hospital Basel during the study period. We successfully generated 468 high quality genomes from unique patients and called variants with our COVID-19 Pipeline (COVGAP), and analysed viral genetic diversity using PANGOLIN taxonomic lineages. To identify introduction and dissemination events we incorporated global SARS-CoV-2 genomes and inferred a time-calibrated phylogeny. Epidemiological data from patient questionnaires was used to facilitate the interpretation of phylogenetic observations. The early outbreak in Basel was dominated by lineage B.1 (83·6%), detected first on March 2nd, although the first sample identified belonged to B.1.1. Within B.1, 68·2% of our samples fall within a clade defined by the SNP C15324T ('Basel cluster'), including 157 identical sequences at the root of the 'Basel cluster', some of which we can specifically trace to regional spreading events. We infer the origin of B.1-C15324T to mid-February in our tri-national region. The other genomes map broadly over the global phylogenetic tree, showing several introduction events from and/or dissemination to other regions of the world via travellers. Family transmissions can also be traced in our data. A single lineage variant dominated the outbreak in the Basel area while other lineages, such as the first (B.1.1), did not propagate. A mass gathering event was the predominant initial source of cases, with travel returners and family transmissions to a lesser extent. We highlight the importance of adding specific questions to epidemiological questionnaires, to obtain data on attendance of large gatherings and their locations, as well as travel history, to effectively identify routes of transmissions in up-coming outbreaks. This phylogenetic analysis in concert with epidemiological and contact tracing data, allows connection and interpretation of events, and can inform public health interventions. Trial Registration: ClinicalTrials.gov NCT04351503

External validation of the PAGE-B score for HCC risk prediction in people living with HIV/HBV coinfection

Background & Aims: HBV coinfection is common among people living with HIV (PLWH) and is the most important cause of hepatocellular carcinoma (HCC). While risk prediction tools for HCC have been validated in patients with HBV monoinfection, they have not been evaluated in PLWH. Thus, we performed an external validation of PAGE-B in people with HIV/HBV coinfection. Methods: We included data on PLWH from four European cohorts who were positive for HBsAg and did not have HCC before starting tenofovir. We estimated the predictive performance of PAGE-B for HCC occurrence over 15 years in patients receiving tenofovir-containing antiretroviral therapy. Model discrimination was assessed after multiple imputation using Cox regression with the prognostic index as a covariate, and by calculating Harrell's c-index. Calibration was assessed by comparing our cumulative incidence with the PAGE-B derivation study using Kaplan-Meier curves. Results: In total, 2,963 individuals with HIV/HBV coinfection on tenofovir-containing antiretroviral therapy were included. PAGE-B was <10 in 26.5%, 10–17 in 57.7%, and ≥18 in 15.7% of patients. Within a median follow-up of 9.6 years, HCC occurred in 68 individuals (2.58/1,000 patient-years, 95% CI 2.03–3.27). The regression slope of the prognostic index for developing HCC within 15 years was 0.93 (95% CI 0.61–1.25), and the pooled c-index was 0.77 (range 0.73–0.80), both indicating good model discrimination. The cumulative incidence of HCC was lower in our study compared to the derivation study. A PAGE-B cut-off of <10 had a negative predictive value of 99.4% for the development of HCC within 5 years. Restricting efforts to individuals with a PAGE-B of ≥10 would spare unnecessary HCC screening in 27% of individuals. Conclusions: For individuals with HIV/HBV coinfection, PAGE-B is a valid tool to determine the need for HCC screening. Impact and implications: Chronic HBV infection is the most important cause of hepatocellular carcinoma (HCC) among people living with HIV. Valid risk prediction may enable better targeting of HCC screening efforts to high-risk individuals. We aimed to validate PAGE-B, a risk prediction tool that is based on age, sex, and platelets, in 2,963 individuals with HIV/HBV coinfection who received tenofovir-containing antiretroviral therapy. In the present study, PAGE-B showed good discrimination, adequate calibration, and a cut-off of <10 had a negative predictive value of 99.4% for the development of HCC within 5 years. These results indicate that PAGE-B is a simple and valid risk prediction tool to determine the need for HCC screening among people living with HIV and HBV

Global Genomic Analysis of SARS-CoV-2 RNA Dependent RNA Polymerase Evolution and Antiviral Drug Resistance.

A variety of antiviral treatments for COVID-19 have been investigated, involving many repurposed drugs. Currently, the SARS-CoV-2 RNA-dependent RNA polymerase (RdRp, encoded by nsp12-nsp7-nsp8) has been targeted by numerous inhibitors, e.g., remdesivir, the only provisionally approved treatment to-date, although the clinical impact of these interventions remains inconclusive. However, the potential emergence of antiviral resistance poses a threat to the efficacy of any successful therapies on a wide scale. Here, we propose a framework to monitor the emergence of antiviral resistance, and as a proof of concept, we address the interaction between RdRp and remdesivir. We show that SARS-CoV-2 RdRp is under purifying selection, that potential escape mutations are rare in circulating lineages, and that those mutations, where present, do not destabilise RdRp. In more than 56,000 viral genomes from 105 countries from the first pandemic wave, we found negative selective pressure affecting nsp12 (Tajima's D = -2.62), with potential antiviral escape mutations in only 0.3% of sequenced genomes. Potential escape mutations included known key residues, such as Nsp12:Val473 and Nsp12:Arg555. Of the potential escape mutations involved globally, in silico structural models found that they were unlikely to be associated with loss of stability in RdRp. No potential escape mutation was found in a local cohort of remdesivir treated patients. Collectively, these findings indicate that RdRp is a suitable drug target, and that remdesivir does not seem to exert high selective pressure. We anticipate our framework to be the starting point of a larger effort for a global monitoring of drug resistance throughout the COVID-19 pandemic